1. Field of the Invention
The invention pertains to a method for detecting a change in mass with an impedance-scanning quartz crystal microbalance and to a device for detecting a change in mass.
2. Description of the Related Art
Quartz crystal microbalances (QCM) are known from the prior art as a means of detecting extremely small changes in mass. The core element of a quartz crystal microbalance is a quartz resonator, which can be caused to vibrate at a resonance frequency by the application of an alternating voltage. Because of the high quality of quartz resonators and the associated stability of their frequencies, they are used in many electronic devices as a time standard. Quartz crystal microbalances (QCM) have already been used for some time in the analytical areas of chemistry, biology, electrochemistry, and materials testing.
In 1959, Günter Sauerbrey defined the relationship between the change in frequency of the oscillation of the quartz crystal and the change in the mass density for the first time. The frequency changes in linear fashion with the change in the mass density on the quartz crystal.
There are basically two different types of quartz crystal microbalances in commercial use—first, the oscillator type, and, second, the impedance-scanning type. The quartz crystal microbalance based on the oscillator design consists, in terms of its circuitry, of an electronic oscillator in a free-running configuration, wherein the mass-detecting quartz crystal is used as the frequency-determining component. FIG. 1 shows a typical impedance curve in the form of a Bode diagram for a quartz resonator of this type.
The phase shift from −90° to +90° and back to −90° again is especially easy to see when there is almost no load on the crystal in air. The first shift (with increasing frequency) is found at the so-called series resonance frequency (vs) of the quartz crystal; the second shift occurs at the so-called parallel resonance frequency (vp). The magnitude is either at a global minimum or at a global maximum at these points.
Conventional oscillator circuits like those found in most quartz crystal microbalances require a phase shift through 0° to ensure that they will function electronically in trouble-free fashion. If the quartz crystal is highly damped as a result of having been introduced into a liquid, for example, the dynamics of the phase shift are considerably reduced—the quartz crystal microbalance no longer functions in a mathematically trivial manner. Extensions to encompass the entire shift of the phase position so that a phase shift through 0° takes place again are complicated and subject to error.
It is also often necessary to compensate manually for parasitic capacitance, which is disadvantageous especially when the goal is to perform efficient, automated measurements.
In the undamped case, the resonance frequency, which is determined by frequency measuring devices, is defined in nearly unique fashion by an abrupt change in the phase behavior (compare FIG. 1, curve A).
In the damped case, the slope of the phase shift is flattened considerably (compare FIG. 1, curve B), and the positions of the resonance frequencies lose their unique quality. Parasitic and unavoidable phase shifts caused by the electronic layout also contribute to a decrease in the accuracy of the frequency—the quality of the oscillator is reduced.
Another approach is to measure the change in impedance as shown in FIG. 1. Complicated and accurate electronic devices are required to do this. These can be either known network analyzers or specialized designs. Common to all of them is that the data obtained, such as the magnitude and phase as a function of frequency, must be converted into an analytically evaluatable form.
To do this, a mathematical model of an electronic equivalent circuit, to which the data can be fitted by nonlinear regression, is required. The BvD model (Butterworth-van Dyke equivalent circuit of a quartz resonator) and its modifications are used for this purpose. The disadvantage of this method is that the measurements proceed very slowly, and in some cases several seconds are required per measurement point. This makes in-situ and real-time measurements impossible, especially when several thousand measurement points must be measured to obtain, for example, highly resolved frequency data.
Fitting to the BvD model, furthermore, is highly unreliable and slow because of the methodology of nonlinear approximation. The basic model (BvD model) is subject to a large number of approximations and assumptions. The course of the fit is highly dependent on the starting and ending frequencies (frequency window). When there are up to ten parameters to be fitted and up to 100,000 measurement points, the process takes a great deal of time. In some cases the fit converges poorly or not at all. The quality of the result, furthermore, is very poor. The starting parameters required are very difficult to estimate, because variables which are difficult if not impossible to observe experimentally are contained in them. The positive course of the fit itself is especially dependent on these starting parameters.
This method therefore makes available a large number of interpretable electrical parameters, but it is difficult or impossible to use it to obtain rapid in-situ measurements.